Aircraft: COMMERCIAL FIXED WING
Phase of flight: Landing
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy

Aircraft X departed Runway 30 on an assigned 270 heading. Shortly after switching the aircraft to departure; I scanned the radar and saw Aircraft X turning through a 270 heading and continuing a left turn to the east directly into the arrival corridor for aircraft landing Runways 1L and 1C. At that moment; a controller at PCT; I think Departure Control contacted me. My initial thought was that Aircraft X had misunderstood my assigned heading and had not switched to Departure Control and was still on my frequency. While the controller was speaking to me other aircraft were talking on the frequency. The cross-talk prevented me from clearly understanding the information that was being relayed in the coordination. I heard the controller say climb the aircraft to 3;000 ft.; and turn him to the west immediately.Because I did not clearly hear the call sign of the aircraft he was referencing my mind jumped to Aircraft X as the aircraft needing the instructions. I immediately issued a climb and turn to Aircraft X and began issuing traffic alerts. Midway through issuing the traffic alerts I recognized that Aircraft X was descending and turning to join final for Runway 1L. In that instance I recognized what Departure Control was trying to coordinate and I sent Flight Number X around and vectored him away from Aircraft X and issued a traffic alert.Aircraft X checked onto my frequency on a mile final. I cleared him to land. Immediately after clearing him to land; the ASDE-X alerted with a taxiway proximity alert. It appeared to me that Aircraft X was correcting back toward Runway 1L. I asked the pilot if they requested priority handling. The pilot said no. The aircraft appeared aligned with the runway and the pilot confirmed they were; but because he was not a priority. I sent the plane around as required by the 7110.65. Coordination would have been easier and clearer had the radar data tag scratchpad entry for Aircraft X been changed to '01L' which would have indicated that he was inbound to land. The scratchpad showed the SID he filed; which contributed to my initial thinking that he was off course and not a priority. Additionally; had Departure Control requested priority handling in the coordination; I believe I would have immediately keyed onto the fact that Aircraft X was returning.The Airport Surface Detection Equipment (ASDE-X) ASDE Taxiway Arrival Prediction Software (ATAP) has had five alerts since its implementation on Date. In every case; the aircraft have been properly aligned with the runway and the alerts have been the result of poorly designed taxiway capture zones. The ATAP enhancement should be temporarily disabled and a full review of the ATAP system should occur. A Tower Local Controller reported a departure deviated from its clearance and turned back to the airport to land and into confliction with an arrival on final approach.The Tower received an alert from an automated system (ASDE X ATAP) warning that the aircraft was aligned with a taxiway and not the runway although the aircraft had corrected back to course. The reporter states that false alerts from the ASDE X ATAP (Airport Surface Detection Equipment Taxiway Arrival Prediction Software) is a recurring issue.